Edumania-An International Multidisciplinary Journal
Vol-02, Issue-04 (Oct -Dec 2024)
An International scholarly/ academic journal, peer-reviewed/ refereed journal, ISSN : 2960-0006
Investigating Algebraic Simple Groups With Conjugacy Classes And Products
Anju
Research Scholar, Department of Mathematics, NIILM University, Kaithal (Haryana)
Jakhar, Manjeet Singh
Associate Professor, Department of Mathematics, NIILM University, Kaithal (Haryana)
DOI: https://doi.org/10.59231/edumania/9092
Page Number: pp. 329-335
Subject: Group Theory, Abstract Algebra, Finite Simple Groups, Conjugacy Classes, Algebraic Structures, Pure Mathematics
Received: 09 August 2024
Accepted: 06 September 2024
Published: 01 October 2024
Thematic Classification: Physical Sciences: Mathematics; Algebra; Group Theory
Abstract
Algebraic simple groups, being non-abelian and lacking proper normal subgroups, represent a profound and captivating domain within group theory and algebraic geometry. In the pursuit of understanding these enigmatic entities, the study of conjugacy classes and products emerges as a key to unlocking their underlying symmetries and structures. Group members can be partitioned into different sets with the use of conjugacy classes, which group together equivalent elements under inner automorphisms to show similar algebraic features. The analysis of conjugacy classes provides deep insights into the dynamics and character of algebraic simple groups. On the other hand, group products explore the interactions between distinct elements, generating new elements within the group and unraveling its internal symmetries.
Keywords:Conjugacy,Algebraic, Groups, Products,Semisimple
Impact Statement
Member of the same conjugacy class cannot be distinguished by using only the group structure, and therefore share many properties. The study of conjugacy classes of non-Abelian group is fundamental for the study of their structure for an abelian group, each conjugacy class is a set containing one element (Singleton Set).
About The Author
My particular pleasure is pure mathematics. I have found mathematics a fascinating subject since my early years. I enjoy it as it is challenging and logical. I look forward to university life and facing both the academic and social challenges head-on. I am confident that my passion for the subject matter, diligence and enthusiasm will allows me to not only be a successful Student, but ultimately to pursue a successful Career in business upon these foundations.
Cite this Article
APA (7th ed.): Anju, & Jakhar, M. S. (2024). Investigating Algebraic Simple Groups With Conjugacy Classes And Products. Edumania-An International Multidisciplinary Journal, 2(4), 329–335. https://doi.org/10.59231/edumania/9092
Chicago (17th ed.): Anju, and Manjeet Singh Jakhar. “Investigating Algebraic Simple Groups With Conjugacy Classes And Products.” Edumania-An International Multidisciplinary Journal 2, no. 4 (2024): 329–335. https://doi.org/10.59231/edumania/9092.
MLA (9th ed.): Anju, and Manjeet Singh Jakhar. “Investigating Algebraic Simple Groups With Conjugacy Classes And Products.” Edumania-An International Multidisciplinary Journal, vol. 2, no. 4, 2024, pp. 329–335. https://doi.org/10.59231/edumania/9092.
Statements & Declarations
Peer Review: The scholarly quality and contribution of this research on algebraic simple groups have been confirmed through a rigorous and independent peer-review process conducted by experts in the relevant fields.
Review Type: This article underwent a double-blind peer review, wherein the identities of the authors (Anju and Manjeet Singh Jakhar) and the reviewers were concealed from each other. The review was conducted by subject experts in abstract algebra, group theory, and pure mathematics.
Competing Interests: The authors, Anju and Manjeet Singh Jakhar, jointly and individually declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Data Availability: All data generated or analyzed during this study, including the mathematical proofs and theoretical derivations, are fully included within this published article. This is a theoretical mathematics paper and does not rely on external datasets.
Funding: The authors received no specific financial support, grants, or funding from any public, commercial, or not-for-profit organization for the research, authorship, and/or publication of this article. The work was completed as part of the authors’ research affiliation with NIILM University, Kaithal.
License: This article is an open-access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives (CC BY-NC-ND) 4.0 International License. This license allows others to download this work and share it with others for non-commercial purposes, as long as they credit the authors, but they cannot change it in any way or use it commercially.
Ethical Approval: Ethical approval was not required for this study, as it is a theoretical mathematics work and did not involve the collection of data from, or experimentation on, human subjects or animals. The work adheres to the highest standards of academic integrity and research ethics in mathematical sciences.
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